nm0775: let me begin by resuming where we finished yesterday we're talking about the concept of elasticity in particular we were looking at the price elasticity of demand we've looked at a number of applications and seen the empirical relevance of this but everything we've done before last time was to talk ra-, in rather vague imprecise terms about the elasticity being a measure of the responsiveness of for example demand to change in price towards the end of last time we started making this concept of ena-, elasticity a more precise quantitative measure and where we got to at the end of last time was to this point here we said we can define the price elasticity of demand as being the proportional change in quantity demanded divided by the prop-, proportional change in price and we can see that easily in terms of the demand curve we start off at some point A we said initial price is P-zero price falls to P-one so delta-P is the change in price and that induces a movement down the demand curve to point B the quantity demanded increasing from Q-zero to Q-one so delta-Q measures the increase in quantity and we're saying the elasticity is measured by this change in quantity divided by the original quantity which is the proportional change all divided by this change in price itself divided by the initial price level which gives us the proportional change in price and i said that therefore that gives us a formula for calculating the elasticity between two points which i said can be defined as the arc or the interval elasticity of demand and what i want to show now are two properties of this elasticity the first property is that clearly the elasticity is negative if the elasticity is negative quite obviously because the demand curve is downward sloping and so if delta-Q is positive because the demand has increased that must be because the price has fallen so if delta-Q is positive that's because delta-P the change in price is negative Q and P themselves are positive numbers we assume if we're starting with a positive price and a positive quantity being demanded and so delta-Q is positive Q is positive P is positive and delta-P is negative so the whole thing is negative the elasticity demand is negative let me ask you to tell me when that might not be the case can you think of a case not necessarily thinking of an example of any particular commodity what would the demand curve have to look like for the elasticity not to be a negative number point here sm0776: when the demand is constant nm0775: when demand is constant so let's look at that in the diagram if the demand is a horizontal straight line is the answer that we're given here then imagine a horizontal straight line that would mean that this change in quantity could be very big even if effectively the change in price was close to zero or essentially zero it approximated zero so that would be saying that delta-P would be zero er let's think about that answer is that is that a good answer well the demand curve being completely flat would mean that demand is completely responsive to small changes in price so it's infinitely elastic delta-P if delta-P is zero this whole thing is zero so if delta if delta-P is is zero this whole thing is infinite and it's actually minus-infinite so it doesn't give us the answer it's not negative it gives us the answer it's infinity albeit minus-infinity okay so what would be another possible response a hand up at the back here sf0777: demand curve nm0775: okay i'm being told to draw demand curve not as a straight line but as a hyperbola using very technical words that's the case i'm going to go on to in a minute i started looking at two properties i've said notice A in a moment i'm going to say notice B and that's going to be to do with exactly the case you mentioned so i'll come on to that in a moment any other thoughts on this A point here sm0778: if er the demand curve is upward sloping nm0775: okay well if the demand curve is upward sloping then clearly everything i've said here is wrong if the demand curve is upward sloping then we can have that when the price if the price increases the quantity demanded will increase and so this will be a positive number so to get a positive elasticity we need an upward sloping demand curve which we're going to say is rather unusual less unusual would be the case where the demand curve is perfectly vertical if the demand curve is perfectly vertical then we're saying that demand is inelastic perfectly inelastic and that would give us an elasticity of zero okay so to have elasticity as not being negative either we have an unusual case that it's positive or we or we have a less unusual case that it's simply vertical so the elasticity is zero so let's but in general we're going to assume demand curves are downward sloping and so we're going to have this property consider now the second property the second property of the elasticity of this demand curve is that the elasticity changes as we move along the demand curve and i want to see how let me just give you a reminder everything i'm saying here relates to this demand curve that i've drawn in the diagram it's a linear demand curve it's a downward sloping straight line or linear demand curve i haven't yet got onto the case i was invited to think about by the contribution at the back the case where the demand curve is not a straight line we'll look at that in a moment for now we assume the demand curve is a straight line and we can show that in that case the elasticity changes as we move along the demand curve okay i'm just i can't always be sure of having two overheads so sometimes i repeat things there's no reason why you should here i just repeat what we've already seen in this first line and then i rearrange this first line 'cause a fraction divided by a fraction is a rather awkward thing to deal with and so we can rearrange it to get a fraction multiplied by a different fraction which is less awkward to deal with if you're not happy with the step going from here to here check it out afterwards okay so i've re-, rewritten or rearranged this expression in the following way when we do that we can now think of these two terms separately think first of all about this first term delta-Q divided by delta-P what can you tell me about this first term as we move along the demand curve what happens to delta-Q over delta-P as we move along the demand curve does it rise does it fall does it stay unchanged what happens any thoughts someone said me an answer here sm0779: it remains constant nm0775: it remains constant absolutely delta-Q over delta-P stays constant along the straight line demand curve we can see that easily in this diagram here the slope of this line slope of this demand curve is given by the gradient of course if you think about point B for a moment it's easiest to th-, to see things in terms of point B address point B and think well what is the slope of this line well in going from B to A the rise is the change in price and the tread the distance travelled is the change in quantity so delta-P over delta-Q is the slope of this straight line demand curve measured against the vertical axis and of course the slope of a straight line demand curve doesn't change so delta-P over delta-Q doesn't change as you move along the demand curve and hence delta-Q over delta-P which is the inverse of the slope or if you like it's the slope of the demand curve measured against the horizontal axis that doesn't change as you move along the demand curve so the first term in this expression for inelasticity is a constant what about the second term what can you tell me about P-over-Q the second term in that expression of elasticity as we move along the demand curve any thoughts or suggestions okay sm0780: as P rises Q falls nm0775: okay sm0780: nm0775: well as we're moving down let's think about moving down the demand curve so moving from A to B to C to D of course what we know is happening is the price is falling and quantity is rising so moving down the demand curve from A down in the direction of D this thing P-over-Q is falling in other words as i've written here so in terms of our expressions being er for the elasticity along the straight line demand curve the first term is constant the second term is falling and so the elasticity is falling as we move down the demand curve if you wanted a further way of seeing this i invite you afterwards to to draw the horizontal lines from the axis the P axis to C and to D and to call that the change in price then drop down the vertical lines and that's the new change in quantity necessarily comparing this move from A to B with this move from C to D delta-P over delta-Q won't have changed but P-over-Q will have changed and so will have a different elasticity okay so with this the conclusion is with a straight line demand curve the elasticity is falling as we move down the demand curve then we might ask a question so what would the demand curve have to look like for this elasticity not to be changing well we know that P-over-Q must be falling as we move down the demand curve P-over-Q must be falling so we need delta-Q over delta-P to be rising okay it's no good if delta er delta-Q stays constant so one thing you might think about doing afterwards is doing what the suggestion was at the back drawing the demand curve not as a straight line but as a hyperbola drawing it like this where if you carried on it asymptotically approaches in other words gets closer and closer to each axis do the same experiment here that we did over here draw points A and B C and D well these two points are having an interval between them the same as those two points of course P-over-Q is fall-, i'm using Q aren't i P-over-Q is falling think what's happening to delta-Q over delta-P and see if that's given you an elasticity which doesn't change so that's the thing to think about afterwards okay for the conclusion i'm giving you is is the following okay so this now is going to conclude my discussion of e-, of elasticities for now we know that so long as the demand curve is downward sloping this th-, this is going to be true whether it's linear or a hyperbola or it doesn't matter as long as it's downward sloping we're assuming that the elasticities are not positive they are less than or equal to zero think about all points between all negative points less than or all points less than or equal to zero okay so start off at zero and think about all the points going down to minus-infinity which was one of the points that was raised earlier in this lecture then if the elasticity is exactly equal to zero we can of course talk about zero elasticity going to make that a bit sharper we can talk about zero elasticity a point further down this scale would be where the elasticity of demand price elasticity of demand is exactly equal to minus-one we talk about that as being unit elasticity think about unit elasticity in our example here i'm just going to put this slide underneath the continuous sheet think about this being equal to minus-one if you then rearranged this expression we get delta-Q over Q equal to minus- delta-P over P so if the elasticity is equal to minus-one in other words if we're dealing with unit elasticity then that's just the same thing as saying that the proportional increase in quantity demanded will be exactly equal to the proportional change in price okay so in other words if for example prices go up by ten per cent and quantity demanded falls by ten per cent then we're talking about unit elasticity so that's what this means as we move down towards minus-infinity we talk about demand being perfectly elastic with respect to changes in price and we distinguished between these two ranges either side of minus-one in the following way any elasticity between zero and minus-one we talk about as being relatively inelastic demand is relatively inelastic and if elasticity is greater than minus-one we talk about it being relatively elastic or elastic for shorthand okay i just want to finish this topic with one small er note of caution in interpreting inelasticity think about this range where demand is inelastic if demand is in this r-, in this range here demand elasticity is in this range here then we say that elasticity is less than nought and greater than minus-one so it's a number like minus-a-half or minus-a-quarter or minus-point-one or minus-comma-one depending on how you denote these things we often talk about the absolute size of elasticity we often think well we know that demand elasticity's a negative number let's not keep referring to it as a negative number let's think about it just as the absolute number to do that we denote it as the elasticity with these two vertical lines either side of it to remind us that we're just dealing with the the absolute number whether it's a half or a quarter or point-one dropping the minus sign and we say that the absolute size of this elasticity is a number which is less than one it's a half or a quarter et cetera and of course when you do that when you cha-, when you drop the minus sign you then talk about a-, demand being more elastic as we're moving in this direction so it's more elastic as the as the number's going from a half from nought through a quarter to a half three-quarters et cetera so the absolute size of the elasticity is getting bigger as we're moving in this direction so there's a slight confusion which i'd usually like to go away and think about be aware that when we talk about demand becoming more elastic it means that the elasticity's becoming more negative it's go-, it's going from a half to a quarter to a half to three-quarters to s-, to six to eight et cetera all on this negative scale so the absolute size grows as it becomes a bigger negative number so that's a point to go away and and reflect on and be sure you've you've er followed and then we can do the same thing for el-, for a for an elastic for the elastic range as well of course and that concludes all i want to say about this topic and i now want to move on to a whole new topic which is topic three of the lecture course nm0775: okay i want us to go for another sorry there's one question can we can everyone be quiet so i can hear the question please sf0781: what's the point of the elasticity what what what do we use all this for nm0775: what do we use it all for we use it for two things one is all those things we've already looked at it's for which is looking at er how for example the impact of minimum wage on the la-, on the labour market okay very topical issue in British political economy at the moment is that there's a new government which is bringing in er minimum wage legislation okay let's just remind ourselves of er of the of this of the diagram for this case let's have a look at a model of the labour market we've got wages and employment our demand curve is demand for labour by firms and there's some supply of labour by workers that would be the equilibrium wage this would be the equilibrium employment level assume that this is what's happening in the British labour market at the moment there is an equilibrium wage there's an equilibrium level of employment and the government is introducing a minimum wage legislation suppose that the w-, the wage legislation will be sufficiently high that's the minimum wage W-lower-bar a floor wage assume it's higher than the equilibrium wage then what will be the effect of this on the labour market very important point in British political economy at the moment and a number of critics of the minimum wage policy are saying that such an action by the government will reduce employment because the equilibrium will go from the market equilibrium A to the regulated equilibrium of point B where demand which is the short side of the market rations the outcome rations the number of jobs down to L-bar the employment level after the impact of the minimum wage okay so this looks like the minimum wage causes a big reduction in the number of jobs causes a lot of unemployment and that's what a lot of critics of the minimum wage are saying will happen one thing we're going to look at through this term is developing an economic analysis which enables us to look at more and more aspects of the minimum wage but in this simple model the effects look as if potentially they might be disastrous for jobs one question we can address within this framework is well how big will be this reduction in the number of jobs my question to you is well what does it depend on we've already seen it someone like to remind us okay what does the magnitude of job loss depend upon within this analysis sm0782: the demand nm0775: the demand sm0782: nm0775: is depe-, er on er a-, and on what in particular of the demand curve sm0782: slope nm0775: the slope and I-E the thing we've been looking at the elasticity of demand okay so we've seen how the slope of the demand curve is related to this concept of elasticity we've said how if demand is very elastic this demand curve is flat and so point B would be further to the left along W-bar okay do you understand that am i going to draw it yes i'm going to draw it suppose in other words that the demand were more elastic not inelastic where let's say mo-, suppose the demand were more elastic then point B would have been here call it B-dash and the job loss would have been greater so the ela-, the the price elasticity of demand which in the labour market means the wage elasticity of demand for labour is a crucial parameter in determining the impact of this important policy on the labour market that's why it's important and but but just in passing we've said that that's just one application we've been looking at a number of applications and that the important one was for the impact of taxation on commodities and indeed we looked at a case of taxation on the labour market okay so let me now go on to the third topic and let me link this third topic with what we've been doing so far topic one was a general introduction to economic phenomena economic methodology et cetera topic in topic two we said let's deri-, let's er assume something called a demand curve don't bother drawing this for the umpteenth time if you just let me put it for you i vary between whether i use Q or X for quantity forgive me but it's the same thing we add we then added a supply curve and we said look where those intersect we have a market equilibrium potentially and we looked at the possible properties of market equilibria in terms of existence uniqueness stability and we looked at comparative static properties of the equilibrium meaning we shifted one of the curves and looked at what happened for price and quantity outcomes but all we did was assume that in a market economy there are such things as demand and supply curves we said their slopes matter because their elasticities matter we didn't address the issue of where these demand and supply curves come from and what we're going to do in topic three is say well where does this demand curve come from how do we derive this demand curve and from that what are its likely properties then in topic four and beyond we're going to say well what about this concept of a supply curve where does that come from what assumption does that make about supplying agents about the motivations of firms and the decisions of firms having gone through the analyses of deriving demand and supply we'll then further address this issue of how these two things interact to give us a market equilibrium because we'll say how does the nature of the market place in which these agents trade how does that determine the nature of the outcome so we'll ask questions about the nature of markets in particular we'll focus on issues of does the outcome depend upon how many agents there are demanding this commodity and or supplying this commodity so that's a scheme of of how we what we've been doing so far links in with what we're going to be doing from now onwards and there's one more thing i i might say before going on into topic three and it's the following we're assuming that the two most important groups of agents in the economy for our initial purposes of analysis are households and firms what we're going to be doing in the in topic three is addressing the question of what determines the demand for the commodities X bought by households from firms then in topic four and beyond we're going to address the er other aspect of that which is well what do we know about firms' decisions concerning the supply of X to households all within some market context that later on we'll also be analysing X of course is just one commodity that is traded between these two broad groups what's an what's another commodity that's traded between these two groups sf0783: labour nm0775: labour good just as households are demanding commodities from firms they're supplying labour to firms and the other side of that coin is that firms are demanding labour from households okay so topic three is going to be analysing this topic four onwards is going to be analysing supply and later on in the course we'll look at what determines households' supply of labour and firms' demand for labour those are just two agents of course in the economy a third agent which we've already touched upon earlier in the course would be government for example how does government come into this analysis well you might say that households are demanding goods not only from firms but also from governments so this box might consist not only of firms but also of government 'cause government provides things just as firms do sometimes in a market place sometimes outside of a market place another way in which government would influence this scheme of things would be that the way in which these relationships are determined the relation-, the the nature of the supply and demand relationships and how they interact within a market place itself is regulated or governed by government okay so the very nature in which these things occur we could argue is determined by to some extent at least the nature and role of governments er within the market okay so that's what we're going to go on to to consider let's immediately make a start on topic three which is that as the demand theory or consumer theory in particular we're going to be looking at what determines the properties of demand curves and how those properties follow from assumptions about the behaviour of rational economic agents okay you remember in the very first lecture i touched upon a little bit the concept of rationality what we mean by rationality we're going to use some of that now and develop that and we're going to proceed with this for fifteen minutes and then have a break okay so what are our assumptions about rationality for these purposes well we suppose that individuals who we're going to refer to more generally as rational economic agents for the purposes of their economic activity we assume that they have preferences and we further assume that these preferences have certain properties and what i want us to do is to consider what those properties are first question we should say is first question we should ask is well preferences over what and if you think about yourself you have preferences over a very wide range of different things commodities activities et cetera we're going to be pretty tight in defining our preferences to just lie over two possible commodities so we're going to be talking about preferences by individuals over different combinations of two commodities and those commodities are going to be two goods X and Y you can think about X and Y as being anything you like okay it could be er it could be that the two things which you think of as giv-, as giving you a lot of happiness over which you have preferences are er new clothes and C-Ds or it might be economics lectures and accountancy lectures [laughter] anything you like so i'm going to call those combinations of these two goods X and Y as being bundles you can think of them as baskets of goods think about someone with a basket in which they've got some C-Ds and some new clothes and they're comparing that basket with another basket with different combinations of those two things i'm not going to use the word baskets i'm going to use the word bundles meaning a collection of or a combination of two commodities or two goods which i'll call X and Y we can represent these bundles in a diagram where on the axes we have the amount of X in this bundle and on the vertical axis the amount of Y in this bundle and i've drawn on here two possible points two possible bundles of goods the bundle at A and the bundle at B and i'm saying suppose A is the bundle of goods in which there are two units of Y and two units of X whilst at point B the bundle represented has one unit of Y and four units of X okay so those are two bundles of goods that you m-, as an individual might confront and let's suppose that this individual is asked to state a preference between these two bundles of goods and asked to say which he or she prefers okay now without knowing this person's preferences and without knowing what these commodities are course we can't easily answer it but what what i can do now is to say well what assumptions are we making about the kind of answers that people might give what properties might their answers satisfy and the first property is the property that their preferences are ordinal we'll just discuss this here and then be a little bit more precise about it i'm assuming that when asked this question people can rank their preferences ordinally I-E that we're assuming that the individual is able to answer this question about which bundle A or B he or she prefers in one of the following ways that they might say i prefer B to A sorry i might i i they might say i prefer A to B alternatively they might say i prefer B to A what would be a third possible response sf0784: nm0775: sorry sf0784: if you like them equally nm0775: okay that i like them equally my terminology for that is they might say i'm indifferent between the two i'm equally happy with A as with B okay so we're going to a-, assume that all of those answers are meaningful answers well you might say well that's just that's just kind of obvious but it isn't i hope so obvious because in allowing these possible answers we're ruling out different possible answers such as the following in particular we're ruling out we're ruling out the possibility that an individual says i don't know which of those two things i prefer there might actually be many situations in the real world where that might be the answer i'm sure you've all been in a situation sometime where you've had to make a choo-, a choice between two things and they've either been so similar that it's been hard to choose or they've been so very different from each other it's hard to choose it's most easy i guess to think that if these two goods are so if these two bundles of goods are so very different it it could be hard to make a choice but we're ruling that out we're going to be adopting an assumption that individual rationality from which we're going to derive demand curves individual rationality is such that people can always state a preference in these ways that they never are unable to rank their preferences a-, across bundles no matter how similar or how different those bundles are now i've said here that they're ranking their preferences between those goods ordinally in an ordinal way what do i mean by that well i by ordinal ranking i mean something different from cardinal ranking which i'll define in a second so by assuming that the individuals can rank preferences ordinally we're ruling out the possibility that preferences can be ranked cardinally so what does that mean what that means is that we rule out the possibility that people are able to say things like the following that that given the choice between A and B i am twice as happy as A as i am with B we're saying that that's too strong a requirement we merely want people to say do you prefer A or B we don't want them to say by how much they prefer A to B we're also ruling out the possibility that people can say things like B makes me fifteen units of satisfaction better off than A okay so back in your room on campus in the privacy of your of your own study room you haven't got some kind of thermometer or barometer of your own level of happiness and you can gauge it each day and give it an actual calibrated number and if someone comes to your door and offers you either a takeaway pizza or a takeaway can of er Boddingtons bitter or Coca-cola or whatever er that you're not able to say le-, hang on a minute i'll just measure exactly how much happiness i get from that one and from that one and compare the two so you know which you'd prefer of those two choices but you don't know by how much you don't calibrate cardinally your level of happiness you rank ordinally where things are in a hierarchy but not measured in the way that you measure temperature on a calibrated scale so those are three kinds of of ways of thinking about utility that we're not going to be adopting in our definitions of individual rationality some of you who've done economics before might have come across the idea of er of levels of utility anyway you could even perhaps think of writing an equation which gives you someone's level of utility and when people talk about utility they also sometimes talk about the idea of marginal utility by which they mean if i have an extra unit of X or an extra slice of pizza for example then my utility level for today goes from twenty to twenty-two and so my marginal utility from this extra slice of pizza is two units of utility but we're saying that we don't believe for the purposes of our er analysis of rationality that people can make those kind of judgements so we're ruling out the idea of measuring utility by numbers and that means we're ruling out the idea of measuring marginal utility okay so for most of this course there might be times in which we say well let's look at what happens if we can do that but on the whole we're going to say we don't believe that marginal utility is a meaningful concept that people don't have that way of thinking about their own utility so if you've if you've heard of marginal utility as you all have now 'cause i've just mentioned it forget it for a while that's not our way of dealing with this notion of of preferences okay so the properties we're looking at then the preferences so far are that people can rank their preferences o-, over different bundles their ranking is done in an ordinal not a cardinal way to recap the preferences are complete in the sense that you can compare an individual can compare any two bundles of goods so we've got ordinal ranking of preferences completeness of preferences thirdly you've got non- satiation of preferences we're assuming that individuals' preferences have this property of non- satiation in other words the consumer always prefers more to less of any commodity goes by the idea of you can't have too much of a good thing if a thing gives you happiness then the more of it the better is that always strictly true someone says yes but we don't er okay well you've do-, you've demonstrated by being here that even though there are many other things you could've gone away to do you've decided to come here i don't believe that namex University campus is has nothing else to offer than this you've come here er and that means that on balance it's a good thing okay it might be that might be a dismal experience but you can survive it and maybe see you take away something that will hel-, enable you to do better on the course pass the exams and that will mean you've got a summer without having to bother about resits all these calculations might be there but if that's true is it would be the case that you'd be happy to sit here until May or June doing nothing else maybe with a sleeping bag and and some food supplies coming every now and again course it isn't you can certainly have too much even of such a good thing as an economics lecture if that's true of an economics lecture it's certainly very very true of other commodities i happen to have one or two friends who enjoy er consuming substances like alcohol [laughter] and i know it's terrible for me to admit that but it's true er and er and pizza okay some of my best friends like pizza er and i have some people who are devoted to pizza and eat and and eat nothing else but even they get to some point where if you offer them an extra slice of pizza they'd have to turn it down because it's no longer giving them positive levels of happiness it's having quite contrary effects on their physiological well-being okay so it certainly is unreasonable to assume that this is always true but for now we're going to assume it one fourth and final property of preferences that i want to introduce before pausing for a break is the property of transitivity we're assuming that peoples' preferences have this property of being transitive now what we mean by this let me introduce the following notation this sign here which is a bit like a a greater than sign with a slight twist is to be read as in the to be read in the following way if the individual prefers A to B okay so that's read as if A is preferred to B or if if the individual prefers A to B and if the individual prefers B to C then by transitivity it follows that the individual must prefer A to C okay so i go along to one individual and i say to him er point A is you have a ticket to go to the next home match of namex er bundle B is you get a free pizza from me and bundle C is you get four tickets for the national lottery there's A B and C if i offer you the choice between A and B do you want to go to er namex or do you want the pizza and if you say pizza and then i offer you the choice between the pizza and the national lottery tickets and you say the national lottery tickets if i then say to you okay what now about the choice between namex and the national lottery tickets if you said ah well in that case namex i say your your preferences are intransitive they don't satisfy this assumption of transitivity and i regard that as for these purposes not satisfying my conditions for rationality so this element of rationality imposes transitivity let me just say one more thing about transitivity before pausing it's true of strict preference it's true in this relationship between preferring one thing to another it's also true of the indifference relationship if asked the same questions the answer was i'm indifferent between A and B okay so this is this reads as if the individual is indifferent between A and B and if they're indifferent between B and C then again by transitivity upper case T is my shorthand for transitivity the individual must also report being in er having transitive er having indifference between A and C if their preferences are transitive okay think about this property of transitivity which you mostly might not have come across before think about something which is think about some phenomenon in the real world which does have transitivity one example would be people's heights if i compared three people A B and C A is taller than B B is taller than C it follows in a kind of logical way that A is bigger than C think about some different phenomenon think about football matches and the question is are football results transitive do they satisfy the property of transitivity okay well look again i have friends who are interested in football and some of them are interested in some football competition called the European Champions League or something of the kind er this is a very European arena a global arena so let's think not just about domestic football let's not just think about namex who i believe aren't in the Champions League tomorrow there are some games in the Champions League of European football er in one particular group there is a team which goes by the name of Manchester United and in their first game of that competition they drew with Barcelona in their second game they drew with Bayern Munich tomorrow night Bayern Munich play Barcelona if football results are transitive then Bayern Munich and Barcelona will draw if you believe that that's true you won't be in this lecture theatre you'll be at the bookmakers putting a lot of money on the outcome if you do that you might well be disappointed 'cause football results sadly or mercifully depending on which way you look at it are not transitive okay so that's the phenomenon of transitivity we'll break there and we'll resume in about ten minutes